scholarly journals The finite element solution of second order elliptic problems with the Newton boundary condition

1983 ◽  
Vol 28 (6) ◽  
pp. 430-456
Author(s):  
Libor Čermák
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Elliptic Problems ◽  
Second Order ◽  
Finite Element Solution ◽  
Element Solution ◽  
Second Order Elliptic Problems

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

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